Properties

Label 1950.2.y.e.199.2
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.e.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.232051 + 0.133975i) q^{11} -1.00000i q^{12} +(-3.50000 + 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(-4.96410 + 2.86603i) q^{19} -3.00000i q^{21} +(0.232051 - 0.133975i) q^{22} +(-3.00000 - 1.73205i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(-1.50000 + 2.59808i) q^{28} +(0.732051 - 1.26795i) q^{29} +4.92820i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.133975 + 0.232051i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.96410 + 5.13397i) q^{37} +5.73205i q^{38} +(-3.46410 - 1.00000i) q^{39} +(-3.46410 - 2.00000i) q^{41} +(-2.59808 - 1.50000i) q^{42} +(5.19615 - 3.00000i) q^{43} -0.267949i q^{44} +(-3.00000 + 1.73205i) q^{46} -6.46410 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-1.00000 + 1.73205i) q^{49} -4.00000 q^{51} +(2.50000 + 2.59808i) q^{52} -0.267949i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} -5.73205 q^{57} +(-0.732051 - 1.26795i) q^{58} +(9.92820 - 5.73205i) q^{59} +(0.267949 + 0.464102i) q^{61} +(4.26795 + 2.46410i) q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +0.267949 q^{66} +(0.732051 - 1.26795i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-1.73205 - 3.00000i) q^{69} +(-11.1962 + 6.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} +6.92820 q^{73} +(2.96410 + 5.13397i) q^{74} +(4.96410 + 2.86603i) q^{76} -0.803848i q^{77} +(-2.59808 + 2.50000i) q^{78} -3.07180 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.46410 + 2.00000i) q^{82} -9.46410 q^{83} +(-2.59808 + 1.50000i) q^{84} -6.00000i q^{86} +(1.26795 - 0.732051i) q^{87} +(-0.232051 - 0.133975i) q^{88} +(12.2321 + 7.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +3.46410i q^{92} +(-2.46410 + 4.26795i) q^{93} +(-3.23205 + 5.59808i) q^{94} +1.00000i q^{96} +(-4.19615 - 7.26795i) q^{97} +(1.00000 + 1.73205i) q^{98} +0.267949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 6q^{7} - 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 6q^{7} - 4q^{8} + 2q^{9} - 6q^{11} - 14q^{13} - 12q^{14} - 2q^{16} + 4q^{18} - 6q^{19} - 6q^{22} - 12q^{23} - 4q^{26} - 6q^{28} - 4q^{29} + 2q^{32} + 4q^{33} + 2q^{36} + 2q^{37} - 12q^{46} - 12q^{47} - 4q^{49} - 16q^{51} + 10q^{52} + 6q^{56} - 16q^{57} + 4q^{58} + 12q^{59} + 8q^{61} + 24q^{62} + 6q^{63} + 4q^{64} + 8q^{66} - 4q^{67} - 24q^{71} - 2q^{72} - 2q^{74} + 6q^{76} - 40q^{79} - 2q^{81} - 24q^{83} + 12q^{87} + 6q^{88} + 42q^{89} + 30q^{91} + 4q^{93} - 6q^{94} + 4q^{97} + 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.232051 + 0.133975i 0.0699660 + 0.0403949i 0.534575 0.845121i \(-0.320472\pi\)
−0.464609 + 0.885516i \(0.653805\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) −3.00000 −0.801784
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.96410 + 2.86603i −1.13884 + 0.657511i −0.946144 0.323747i \(-0.895057\pi\)
−0.192699 + 0.981258i \(0.561724\pi\)
\(20\) 0 0
\(21\) 3.00000i 0.654654i
\(22\) 0.232051 0.133975i 0.0494734 0.0285635i
\(23\) −3.00000 1.73205i −0.625543 0.361158i 0.153481 0.988152i \(-0.450952\pi\)
−0.779024 + 0.626994i \(0.784285\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −1.50000 + 2.59808i −0.283473 + 0.490990i
\(29\) 0.732051 1.26795i 0.135938 0.235452i −0.790017 0.613085i \(-0.789928\pi\)
0.925956 + 0.377633i \(0.123262\pi\)
\(30\) 0 0
\(31\) 4.92820i 0.885131i 0.896736 + 0.442566i \(0.145932\pi\)
−0.896736 + 0.442566i \(0.854068\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.133975 + 0.232051i 0.0233220 + 0.0403949i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −2.96410 + 5.13397i −0.487295 + 0.844020i −0.999893 0.0146085i \(-0.995350\pi\)
0.512598 + 0.858629i \(0.328683\pi\)
\(38\) 5.73205i 0.929861i
\(39\) −3.46410 1.00000i −0.554700 0.160128i
\(40\) 0 0
\(41\) −3.46410 2.00000i −0.541002 0.312348i 0.204483 0.978870i \(-0.434449\pi\)
−0.745485 + 0.666523i \(0.767782\pi\)
\(42\) −2.59808 1.50000i −0.400892 0.231455i
\(43\) 5.19615 3.00000i 0.792406 0.457496i −0.0484030 0.998828i \(-0.515413\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(44\) 0.267949i 0.0403949i
\(45\) 0 0
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) −6.46410 −0.942886 −0.471443 0.881897i \(-0.656267\pi\)
−0.471443 + 0.881897i \(0.656267\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 2.50000 + 2.59808i 0.346688 + 0.360288i
\(53\) 0.267949i 0.0368057i −0.999831 0.0184028i \(-0.994142\pi\)
0.999831 0.0184028i \(-0.00585813\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) −5.73205 −0.759229
\(58\) −0.732051 1.26795i −0.0961230 0.166490i
\(59\) 9.92820 5.73205i 1.29254 0.746249i 0.313438 0.949609i \(-0.398519\pi\)
0.979104 + 0.203359i \(0.0651859\pi\)
\(60\) 0 0
\(61\) 0.267949 + 0.464102i 0.0343074 + 0.0594221i 0.882669 0.469995i \(-0.155744\pi\)
−0.848362 + 0.529417i \(0.822411\pi\)
\(62\) 4.26795 + 2.46410i 0.542030 + 0.312941i
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.267949 0.0329823
\(67\) 0.732051 1.26795i 0.0894342 0.154905i −0.817838 0.575449i \(-0.804827\pi\)
0.907272 + 0.420544i \(0.138161\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) −1.73205 3.00000i −0.208514 0.361158i
\(70\) 0 0
\(71\) −11.1962 + 6.46410i −1.32874 + 0.767148i −0.985105 0.171956i \(-0.944991\pi\)
−0.343634 + 0.939104i \(0.611658\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 6.92820 0.810885 0.405442 0.914121i \(-0.367117\pi\)
0.405442 + 0.914121i \(0.367117\pi\)
\(74\) 2.96410 + 5.13397i 0.344570 + 0.596812i
\(75\) 0 0
\(76\) 4.96410 + 2.86603i 0.569422 + 0.328756i
\(77\) 0.803848i 0.0916069i
\(78\) −2.59808 + 2.50000i −0.294174 + 0.283069i
\(79\) −3.07180 −0.345604 −0.172802 0.984957i \(-0.555282\pi\)
−0.172802 + 0.984957i \(0.555282\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.46410 + 2.00000i −0.382546 + 0.220863i
\(83\) −9.46410 −1.03882 −0.519410 0.854525i \(-0.673848\pi\)
−0.519410 + 0.854525i \(0.673848\pi\)
\(84\) −2.59808 + 1.50000i −0.283473 + 0.163663i
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) 1.26795 0.732051i 0.135938 0.0784841i
\(88\) −0.232051 0.133975i −0.0247367 0.0142817i
\(89\) 12.2321 + 7.06218i 1.29659 + 0.748589i 0.979814 0.199910i \(-0.0640648\pi\)
0.316780 + 0.948499i \(0.397398\pi\)
\(90\) 0 0
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 3.46410i 0.361158i
\(93\) −2.46410 + 4.26795i −0.255515 + 0.442566i
\(94\) −3.23205 + 5.59808i −0.333361 + 0.577397i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −4.19615 7.26795i −0.426055 0.737948i 0.570464 0.821323i \(-0.306764\pi\)
−0.996518 + 0.0833745i \(0.973430\pi\)
\(98\) 1.00000 + 1.73205i 0.101015 + 0.174964i
\(99\) 0.267949i 0.0269299i
\(100\) 0 0
\(101\) −6.19615 + 10.7321i −0.616540 + 1.06788i 0.373572 + 0.927601i \(0.378133\pi\)
−0.990112 + 0.140278i \(0.955200\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) 11.5885i 1.14184i −0.821004 0.570922i \(-0.806586\pi\)
0.821004 0.570922i \(-0.193414\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 0 0
\(106\) −0.232051 0.133975i −0.0225388 0.0130128i
\(107\) −11.1962 6.46410i −1.08237 0.624908i −0.150837 0.988559i \(-0.548197\pi\)
−0.931536 + 0.363650i \(0.881530\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 10.3923i 0.995402i 0.867349 + 0.497701i \(0.165822\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(110\) 0 0
\(111\) −5.13397 + 2.96410i −0.487295 + 0.281340i
\(112\) 3.00000 0.283473
\(113\) −10.3923 + 6.00000i −0.977626 + 0.564433i −0.901553 0.432670i \(-0.857572\pi\)
−0.0760733 + 0.997102i \(0.524238\pi\)
\(114\) −2.86603 + 4.96410i −0.268428 + 0.464931i
\(115\) 0 0
\(116\) −1.46410 −0.135938
\(117\) −2.50000 2.59808i −0.231125 0.240192i
\(118\) 11.4641i 1.05536i
\(119\) 10.3923 + 6.00000i 0.952661 + 0.550019i
\(120\) 0 0
\(121\) −5.46410 9.46410i −0.496737 0.860373i
\(122\) 0.535898 0.0485180
\(123\) −2.00000 3.46410i −0.180334 0.312348i
\(124\) 4.26795 2.46410i 0.383273 0.221283i
\(125\) 0 0
\(126\) −1.50000 2.59808i −0.133631 0.231455i
\(127\) −10.9641 6.33013i −0.972907 0.561708i −0.0727855 0.997348i \(-0.523189\pi\)
−0.900121 + 0.435640i \(0.856522\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) 14.3205 1.25119 0.625594 0.780149i \(-0.284857\pi\)
0.625594 + 0.780149i \(0.284857\pi\)
\(132\) 0.133975 0.232051i 0.0116610 0.0201974i
\(133\) 14.8923 + 8.59808i 1.29133 + 0.745548i
\(134\) −0.732051 1.26795i −0.0632396 0.109534i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) −6.73205 11.6603i −0.575158 0.996203i −0.996024 0.0890802i \(-0.971607\pi\)
0.420867 0.907123i \(-0.361726\pi\)
\(138\) −3.46410 −0.294884
\(139\) −9.89230 17.1340i −0.839054 1.45328i −0.890686 0.454619i \(-0.849776\pi\)
0.0516319 0.998666i \(-0.483558\pi\)
\(140\) 0 0
\(141\) −5.59808 3.23205i −0.471443 0.272188i
\(142\) 12.9282i 1.08491i
\(143\) −0.928203 0.267949i −0.0776203 0.0224070i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 3.46410 6.00000i 0.286691 0.496564i
\(147\) −1.73205 + 1.00000i −0.142857 + 0.0824786i
\(148\) 5.92820 0.487295
\(149\) −16.2679 + 9.39230i −1.33272 + 0.769448i −0.985716 0.168415i \(-0.946135\pi\)
−0.347006 + 0.937863i \(0.612802\pi\)
\(150\) 0 0
\(151\) 22.7846i 1.85419i 0.374832 + 0.927093i \(0.377700\pi\)
−0.374832 + 0.927093i \(0.622300\pi\)
\(152\) 4.96410 2.86603i 0.402642 0.232465i
\(153\) −3.46410 2.00000i −0.280056 0.161690i
\(154\) −0.696152 0.401924i −0.0560976 0.0323879i
\(155\) 0 0
\(156\) 0.866025 + 3.50000i 0.0693375 + 0.280224i
\(157\) 21.1962i 1.69164i −0.533471 0.845819i \(-0.679113\pi\)
0.533471 0.845819i \(-0.320887\pi\)
\(158\) −1.53590 + 2.66025i −0.122190 + 0.211638i
\(159\) 0.133975 0.232051i 0.0106249 0.0184028i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −1.46410 2.53590i −0.114677 0.198627i 0.802973 0.596015i \(-0.203250\pi\)
−0.917651 + 0.397388i \(0.869917\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −4.73205 + 8.19615i −0.367278 + 0.636145i
\(167\) −0.232051 + 0.401924i −0.0179566 + 0.0311018i −0.874864 0.484368i \(-0.839049\pi\)
0.856907 + 0.515470i \(0.172383\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 0 0
\(171\) −4.96410 2.86603i −0.379614 0.219170i
\(172\) −5.19615 3.00000i −0.396203 0.228748i
\(173\) −1.83975 + 1.06218i −0.139873 + 0.0807559i −0.568304 0.822819i \(-0.692400\pi\)
0.428430 + 0.903575i \(0.359067\pi\)
\(174\) 1.46410i 0.110993i
\(175\) 0 0
\(176\) −0.232051 + 0.133975i −0.0174915 + 0.0100987i
\(177\) 11.4641 0.861695
\(178\) 12.2321 7.06218i 0.916831 0.529333i
\(179\) 4.53590 7.85641i 0.339029 0.587215i −0.645221 0.763996i \(-0.723235\pi\)
0.984250 + 0.176780i \(0.0565682\pi\)
\(180\) 0 0
\(181\) 16.9282 1.25826 0.629132 0.777299i \(-0.283411\pi\)
0.629132 + 0.777299i \(0.283411\pi\)
\(182\) 10.5000 2.59808i 0.778312 0.192582i
\(183\) 0.535898i 0.0396147i
\(184\) 3.00000 + 1.73205i 0.221163 + 0.127688i
\(185\) 0 0
\(186\) 2.46410 + 4.26795i 0.180677 + 0.312941i
\(187\) −1.07180 −0.0783775
\(188\) 3.23205 + 5.59808i 0.235722 + 0.408282i
\(189\) 2.59808 1.50000i 0.188982 0.109109i
\(190\) 0 0
\(191\) 8.66025 + 15.0000i 0.626634 + 1.08536i 0.988222 + 0.153024i \(0.0489012\pi\)
−0.361588 + 0.932338i \(0.617765\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 4.92820 8.53590i 0.354740 0.614427i −0.632334 0.774696i \(-0.717903\pi\)
0.987073 + 0.160269i \(0.0512361\pi\)
\(194\) −8.39230 −0.602532
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −5.69615 + 9.86603i −0.405834 + 0.702925i −0.994418 0.105511i \(-0.966352\pi\)
0.588584 + 0.808436i \(0.299686\pi\)
\(198\) 0.232051 + 0.133975i 0.0164911 + 0.00952116i
\(199\) −12.4641 21.5885i −0.883557 1.53037i −0.847359 0.531021i \(-0.821809\pi\)
−0.0361978 0.999345i \(-0.511525\pi\)
\(200\) 0 0
\(201\) 1.26795 0.732051i 0.0894342 0.0516349i
\(202\) 6.19615 + 10.7321i 0.435960 + 0.755104i
\(203\) −4.39230 −0.308279
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) −10.0359 5.79423i −0.699234 0.403703i
\(207\) 3.46410i 0.240772i
\(208\) 1.00000 3.46410i 0.0693375 0.240192i
\(209\) −1.53590 −0.106240
\(210\) 0 0
\(211\) 4.03590 6.99038i 0.277843 0.481238i −0.693006 0.720932i \(-0.743714\pi\)
0.970848 + 0.239694i \(0.0770473\pi\)
\(212\) −0.232051 + 0.133975i −0.0159373 + 0.00920141i
\(213\) −12.9282 −0.885826
\(214\) −11.1962 + 6.46410i −0.765353 + 0.441877i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 12.8038 7.39230i 0.869182 0.501822i
\(218\) 9.00000 + 5.19615i 0.609557 + 0.351928i
\(219\) 6.00000 + 3.46410i 0.405442 + 0.234082i
\(220\) 0 0
\(221\) 10.3923 10.0000i 0.699062 0.672673i
\(222\) 5.92820i 0.397875i
\(223\) 9.42820 16.3301i 0.631359 1.09355i −0.355915 0.934518i \(-0.615831\pi\)
0.987274 0.159028i \(-0.0508360\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) −3.26795 5.66025i −0.216901 0.375684i 0.736958 0.675939i \(-0.236262\pi\)
−0.953859 + 0.300255i \(0.902928\pi\)
\(228\) 2.86603 + 4.96410i 0.189807 + 0.328756i
\(229\) 4.53590i 0.299741i −0.988706 0.149870i \(-0.952114\pi\)
0.988706 0.149870i \(-0.0478856\pi\)
\(230\) 0 0
\(231\) 0.401924 0.696152i 0.0264446 0.0458035i
\(232\) −0.732051 + 1.26795i −0.0480615 + 0.0832449i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) −3.50000 + 0.866025i −0.228802 + 0.0566139i
\(235\) 0 0
\(236\) −9.92820 5.73205i −0.646271 0.373125i
\(237\) −2.66025 1.53590i −0.172802 0.0997673i
\(238\) 10.3923 6.00000i 0.673633 0.388922i
\(239\) 3.46410i 0.224074i 0.993704 + 0.112037i \(0.0357375\pi\)
−0.993704 + 0.112037i \(0.964262\pi\)
\(240\) 0 0
\(241\) −21.8205 + 12.5981i −1.40558 + 0.811513i −0.994958 0.100291i \(-0.968023\pi\)
−0.410624 + 0.911805i \(0.634689\pi\)
\(242\) −10.9282 −0.702492
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0.267949 0.464102i 0.0171537 0.0297111i
\(245\) 0 0
\(246\) −4.00000 −0.255031
\(247\) 14.8923 14.3301i 0.947575 0.911804i
\(248\) 4.92820i 0.312941i
\(249\) −8.19615 4.73205i −0.519410 0.299882i
\(250\) 0 0
\(251\) −9.76795 16.9186i −0.616547 1.06789i −0.990111 0.140287i \(-0.955198\pi\)
0.373563 0.927605i \(-0.378136\pi\)
\(252\) −3.00000 −0.188982
\(253\) −0.464102 0.803848i −0.0291778 0.0505375i
\(254\) −10.9641 + 6.33013i −0.687949 + 0.397187i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 12.5885 + 7.26795i 0.785246 + 0.453362i 0.838286 0.545230i \(-0.183558\pi\)
−0.0530400 + 0.998592i \(0.516891\pi\)
\(258\) 3.00000 5.19615i 0.186772 0.323498i
\(259\) 17.7846 1.10508
\(260\) 0 0
\(261\) 1.46410 0.0906256
\(262\) 7.16025 12.4019i 0.442362 0.766193i
\(263\) 21.2321 + 12.2583i 1.30922 + 0.755881i 0.981967 0.189054i \(-0.0605422\pi\)
0.327258 + 0.944935i \(0.393875\pi\)
\(264\) −0.133975 0.232051i −0.00824557 0.0142817i
\(265\) 0 0
\(266\) 14.8923 8.59808i 0.913106 0.527182i
\(267\) 7.06218 + 12.2321i 0.432198 + 0.748589i
\(268\) −1.46410 −0.0894342
\(269\) −8.53590 14.7846i −0.520443 0.901434i −0.999717 0.0237685i \(-0.992434\pi\)
0.479275 0.877665i \(-0.340900\pi\)
\(270\) 0 0
\(271\) 21.1244 + 12.1962i 1.28321 + 0.740863i 0.977434 0.211239i \(-0.0677499\pi\)
0.305779 + 0.952103i \(0.401083\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 2.59808 + 10.5000i 0.157243 + 0.635489i
\(274\) −13.4641 −0.813396
\(275\) 0 0
\(276\) −1.73205 + 3.00000i −0.104257 + 0.180579i
\(277\) −10.0359 + 5.79423i −0.602999 + 0.348141i −0.770220 0.637778i \(-0.779854\pi\)
0.167222 + 0.985919i \(0.446520\pi\)
\(278\) −19.7846 −1.18660
\(279\) −4.26795 + 2.46410i −0.255515 + 0.147522i
\(280\) 0 0
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) −5.59808 + 3.23205i −0.333361 + 0.192466i
\(283\) 5.53590 + 3.19615i 0.329075 + 0.189992i 0.655430 0.755256i \(-0.272487\pi\)
−0.326355 + 0.945247i \(0.605821\pi\)
\(284\) 11.1962 + 6.46410i 0.664369 + 0.383574i
\(285\) 0 0
\(286\) −0.696152 + 0.669873i −0.0411644 + 0.0396104i
\(287\) 12.0000i 0.708338i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 8.39230i 0.491966i
\(292\) −3.46410 6.00000i −0.202721 0.351123i
\(293\) 14.6244 + 25.3301i 0.854364 + 1.47980i 0.877234 + 0.480063i \(0.159386\pi\)
−0.0228698 + 0.999738i \(0.507280\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 0 0
\(296\) 2.96410 5.13397i 0.172285 0.298406i
\(297\) −0.133975 + 0.232051i −0.00777399 + 0.0134650i
\(298\) 18.7846i 1.08816i
\(299\) 12.0000 + 3.46410i 0.693978 + 0.200334i
\(300\) 0 0
\(301\) −15.5885 9.00000i −0.898504 0.518751i
\(302\) 19.7321 + 11.3923i 1.13545 + 0.655553i
\(303\) −10.7321 + 6.19615i −0.616540 + 0.355960i
\(304\) 5.73205i 0.328756i
\(305\) 0 0
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 28.2487 1.61224 0.806120 0.591753i \(-0.201564\pi\)
0.806120 + 0.591753i \(0.201564\pi\)
\(308\) −0.696152 + 0.401924i −0.0396670 + 0.0229017i
\(309\) 5.79423 10.0359i 0.329622 0.570922i
\(310\) 0 0
\(311\) 18.9282 1.07332 0.536660 0.843799i \(-0.319686\pi\)
0.536660 + 0.843799i \(0.319686\pi\)
\(312\) 3.46410 + 1.00000i 0.196116 + 0.0566139i
\(313\) 33.3205i 1.88339i −0.336473 0.941693i \(-0.609234\pi\)
0.336473 0.941693i \(-0.390766\pi\)
\(314\) −18.3564 10.5981i −1.03591 0.598084i
\(315\) 0 0
\(316\) 1.53590 + 2.66025i 0.0864010 + 0.149651i
\(317\) −30.4641 −1.71103 −0.855517 0.517774i \(-0.826761\pi\)
−0.855517 + 0.517774i \(0.826761\pi\)
\(318\) −0.133975 0.232051i −0.00751292 0.0130128i
\(319\) 0.339746 0.196152i 0.0190221 0.0109824i
\(320\) 0 0
\(321\) −6.46410 11.1962i −0.360791 0.624908i
\(322\) 9.00000 + 5.19615i 0.501550 + 0.289570i
\(323\) 11.4641 19.8564i 0.637880 1.10484i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.92820 −0.162178
\(327\) −5.19615 + 9.00000i −0.287348 + 0.497701i
\(328\) 3.46410 + 2.00000i 0.191273 + 0.110432i
\(329\) 9.69615 + 16.7942i 0.534566 + 0.925896i
\(330\) 0 0
\(331\) 12.4641 7.19615i 0.685089 0.395536i −0.116681 0.993169i \(-0.537225\pi\)
0.801770 + 0.597633i \(0.203892\pi\)
\(332\) 4.73205 + 8.19615i 0.259705 + 0.449822i
\(333\) −5.92820 −0.324864
\(334\) 0.232051 + 0.401924i 0.0126973 + 0.0219923i
\(335\) 0 0
\(336\) 2.59808 + 1.50000i 0.141737 + 0.0818317i
\(337\) 26.3923i 1.43768i 0.695175 + 0.718840i \(0.255327\pi\)
−0.695175 + 0.718840i \(0.744673\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) −0.660254 + 1.14359i −0.0357548 + 0.0619291i
\(342\) −4.96410 + 2.86603i −0.268428 + 0.154977i
\(343\) −15.0000 −0.809924
\(344\) −5.19615 + 3.00000i −0.280158 + 0.161749i
\(345\) 0 0
\(346\) 2.12436i 0.114206i
\(347\) −3.80385 + 2.19615i −0.204201 + 0.117896i −0.598614 0.801038i \(-0.704281\pi\)
0.394412 + 0.918934i \(0.370948\pi\)
\(348\) −1.26795 0.732051i −0.0679692 0.0392420i
\(349\) 9.12436 + 5.26795i 0.488416 + 0.281987i 0.723917 0.689887i \(-0.242340\pi\)
−0.235501 + 0.971874i \(0.575673\pi\)
\(350\) 0 0
\(351\) −0.866025 3.50000i −0.0462250 0.186816i
\(352\) 0.267949i 0.0142817i
\(353\) −3.80385 + 6.58846i −0.202458 + 0.350668i −0.949320 0.314311i \(-0.898226\pi\)
0.746862 + 0.664980i \(0.231560\pi\)
\(354\) 5.73205 9.92820i 0.304655 0.527678i
\(355\) 0 0
\(356\) 14.1244i 0.748589i
\(357\) 6.00000 + 10.3923i 0.317554 + 0.550019i
\(358\) −4.53590 7.85641i −0.239730 0.415224i
\(359\) 0.928203i 0.0489887i 0.999700 + 0.0244943i \(0.00779757\pi\)
−0.999700 + 0.0244943i \(0.992202\pi\)
\(360\) 0 0
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) 8.46410 14.6603i 0.444863 0.770526i
\(363\) 10.9282i 0.573582i
\(364\) 3.00000 10.3923i 0.157243 0.544705i
\(365\) 0 0
\(366\) 0.464102 + 0.267949i 0.0242590 + 0.0140059i
\(367\) 18.4641 + 10.6603i 0.963818 + 0.556461i 0.897346 0.441328i \(-0.145492\pi\)
0.0664722 + 0.997788i \(0.478826\pi\)
\(368\) 3.00000 1.73205i 0.156386 0.0902894i
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) −0.696152 + 0.401924i −0.0361424 + 0.0208668i
\(372\) 4.92820 0.255515
\(373\) 7.85641 4.53590i 0.406789 0.234860i −0.282620 0.959232i \(-0.591204\pi\)
0.689409 + 0.724372i \(0.257870\pi\)
\(374\) −0.535898 + 0.928203i −0.0277106 + 0.0479962i
\(375\) 0 0
\(376\) 6.46410 0.333361
\(377\) −1.46410 + 5.07180i −0.0754051 + 0.261211i
\(378\) 3.00000i 0.154303i
\(379\) 8.42820 + 4.86603i 0.432928 + 0.249951i 0.700593 0.713561i \(-0.252919\pi\)
−0.267665 + 0.963512i \(0.586252\pi\)
\(380\) 0 0
\(381\) −6.33013 10.9641i −0.324302 0.561708i
\(382\) 17.3205 0.886194
\(383\) 2.39230 + 4.14359i 0.122241 + 0.211728i 0.920651 0.390386i \(-0.127659\pi\)
−0.798410 + 0.602114i \(0.794325\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) −4.92820 8.53590i −0.250839 0.434466i
\(387\) 5.19615 + 3.00000i 0.264135 + 0.152499i
\(388\) −4.19615 + 7.26795i −0.213027 + 0.368974i
\(389\) −17.8564 −0.905356 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(390\) 0 0
\(391\) 13.8564 0.700749
\(392\) 1.00000 1.73205i 0.0505076 0.0874818i
\(393\) 12.4019 + 7.16025i 0.625594 + 0.361187i
\(394\) 5.69615 + 9.86603i 0.286968 + 0.497043i
\(395\) 0 0
\(396\) 0.232051 0.133975i 0.0116610 0.00673248i
\(397\) 2.96410 + 5.13397i 0.148764 + 0.257667i 0.930771 0.365603i \(-0.119137\pi\)
−0.782007 + 0.623270i \(0.785804\pi\)
\(398\) −24.9282 −1.24954
\(399\) 8.59808 + 14.8923i 0.430442 + 0.745548i
\(400\) 0 0
\(401\) −19.1603 11.0622i −0.956817 0.552419i −0.0616254 0.998099i \(-0.519628\pi\)
−0.895192 + 0.445681i \(0.852962\pi\)
\(402\) 1.46410i 0.0730228i
\(403\) −4.26795 17.2487i −0.212602 0.859220i
\(404\) 12.3923 0.616540
\(405\) 0 0
\(406\) −2.19615 + 3.80385i −0.108993 + 0.188782i
\(407\) −1.37564 + 0.794229i −0.0681882 + 0.0393685i
\(408\) 4.00000 0.198030
\(409\) 33.8205 19.5263i 1.67232 0.965512i 0.705980 0.708232i \(-0.250507\pi\)
0.966337 0.257280i \(-0.0828264\pi\)
\(410\) 0 0
\(411\) 13.4641i 0.664135i
\(412\) −10.0359 + 5.79423i −0.494433 + 0.285461i
\(413\) −29.7846 17.1962i −1.46560 0.846167i
\(414\) −3.00000 1.73205i −0.147442 0.0851257i
\(415\) 0 0
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) 19.7846i 0.968857i
\(418\) −0.767949 + 1.33013i −0.0375616 + 0.0650586i
\(419\) 4.92820 8.53590i 0.240758 0.417006i −0.720172 0.693795i \(-0.755937\pi\)
0.960931 + 0.276790i \(0.0892705\pi\)
\(420\) 0 0
\(421\) 21.8564i 1.06522i −0.846362 0.532608i \(-0.821212\pi\)
0.846362 0.532608i \(-0.178788\pi\)
\(422\) −4.03590 6.99038i −0.196464 0.340286i
\(423\) −3.23205 5.59808i −0.157148 0.272188i
\(424\) 0.267949i 0.0130128i
\(425\) 0 0
\(426\) −6.46410 + 11.1962i −0.313187 + 0.542455i
\(427\) 0.803848 1.39230i 0.0389009 0.0673784i
\(428\) 12.9282i 0.624908i
\(429\) −0.669873 0.696152i −0.0323418 0.0336106i
\(430\) 0 0
\(431\) −12.0000 6.92820i −0.578020 0.333720i 0.182326 0.983238i \(-0.441637\pi\)
−0.760346 + 0.649518i \(0.774971\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) −7.60770 + 4.39230i −0.365602 + 0.211081i −0.671536 0.740972i \(-0.734365\pi\)
0.305933 + 0.952053i \(0.401032\pi\)
\(434\) 14.7846i 0.709684i
\(435\) 0 0
\(436\) 9.00000 5.19615i 0.431022 0.248851i
\(437\) 19.8564 0.949861
\(438\) 6.00000 3.46410i 0.286691 0.165521i
\(439\) −6.66025 + 11.5359i −0.317877 + 0.550578i −0.980045 0.198777i \(-0.936303\pi\)
0.662168 + 0.749355i \(0.269636\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) −3.46410 14.0000i −0.164771 0.665912i
\(443\) 19.8564i 0.943406i −0.881757 0.471703i \(-0.843639\pi\)
0.881757 0.471703i \(-0.156361\pi\)
\(444\) 5.13397 + 2.96410i 0.243648 + 0.140670i
\(445\) 0 0
\(446\) −9.42820 16.3301i −0.446438 0.773254i
\(447\) −18.7846 −0.888482
\(448\) −1.50000 2.59808i −0.0708683 0.122748i
\(449\) 5.30385 3.06218i 0.250304 0.144513i −0.369599 0.929191i \(-0.620505\pi\)
0.619903 + 0.784678i \(0.287172\pi\)
\(450\) 0 0
\(451\) −0.535898 0.928203i −0.0252345 0.0437074i
\(452\) 10.3923 + 6.00000i 0.488813 + 0.282216i
\(453\) −11.3923 + 19.7321i −0.535257 + 0.927093i
\(454\) −6.53590 −0.306745
\(455\) 0 0
\(456\) 5.73205 0.268428
\(457\) −3.73205 + 6.46410i −0.174578 + 0.302378i −0.940015 0.341133i \(-0.889189\pi\)
0.765437 + 0.643511i \(0.222523\pi\)
\(458\) −3.92820 2.26795i −0.183553 0.105974i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) −10.0526 + 5.80385i −0.468194 + 0.270312i −0.715484 0.698630i \(-0.753794\pi\)
0.247289 + 0.968942i \(0.420460\pi\)
\(462\) −0.401924 0.696152i −0.0186992 0.0323879i
\(463\) −40.7846 −1.89542 −0.947711 0.319131i \(-0.896609\pi\)
−0.947711 + 0.319131i \(0.896609\pi\)
\(464\) 0.732051 + 1.26795i 0.0339846 + 0.0588631i
\(465\) 0 0
\(466\) 15.5885 + 9.00000i 0.722121 + 0.416917i
\(467\) 24.3923i 1.12874i −0.825522 0.564371i \(-0.809119\pi\)
0.825522 0.564371i \(-0.190881\pi\)
\(468\) −1.00000 + 3.46410i −0.0462250 + 0.160128i
\(469\) −4.39230 −0.202818
\(470\) 0 0
\(471\) 10.5981 18.3564i 0.488334 0.845819i
\(472\) −9.92820 + 5.73205i −0.456983 + 0.263839i
\(473\) 1.60770 0.0739219
\(474\) −2.66025 + 1.53590i −0.122190 + 0.0705461i
\(475\) 0 0
\(476\) 12.0000i 0.550019i
\(477\) 0.232051 0.133975i 0.0106249 0.00613428i
\(478\) 3.00000 + 1.73205i 0.137217 + 0.0792222i
\(479\) 19.2679 + 11.1244i 0.880375 + 0.508285i 0.870782 0.491669i \(-0.163613\pi\)
0.00959301 + 0.999954i \(0.496946\pi\)
\(480\) 0 0
\(481\) 5.92820 20.5359i 0.270303 0.936356i
\(482\) 25.1962i 1.14765i
\(483\) −5.19615 + 9.00000i −0.236433 + 0.409514i
\(484\) −5.46410 + 9.46410i −0.248368 + 0.430186i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −10.5000 18.1865i −0.475800 0.824110i 0.523815 0.851832i \(-0.324508\pi\)
−0.999616 + 0.0277214i \(0.991175\pi\)
\(488\) −0.267949 0.464102i −0.0121295 0.0210089i
\(489\) 2.92820i 0.132418i
\(490\) 0 0
\(491\) −2.69615 + 4.66987i −0.121676 + 0.210748i −0.920429 0.390911i \(-0.872160\pi\)
0.798753 + 0.601659i \(0.205493\pi\)
\(492\) −2.00000 + 3.46410i −0.0901670 + 0.156174i
\(493\) 5.85641i 0.263759i
\(494\) −4.96410 20.0622i −0.223345 0.902640i
\(495\) 0 0
\(496\) −4.26795 2.46410i −0.191637 0.110641i
\(497\) 33.5885 + 19.3923i 1.50665 + 0.869864i
\(498\) −8.19615 + 4.73205i −0.367278 + 0.212048i
\(499\) 33.3205i 1.49163i 0.666153 + 0.745815i \(0.267940\pi\)
−0.666153 + 0.745815i \(0.732060\pi\)
\(500\) 0 0
\(501\) −0.401924 + 0.232051i −0.0179566 + 0.0103673i
\(502\) −19.5359 −0.871930
\(503\) 3.23205 1.86603i 0.144110 0.0832020i −0.426211 0.904624i \(-0.640152\pi\)
0.570321 + 0.821422i \(0.306819\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) 0 0
\(506\) −0.928203 −0.0412637
\(507\) 12.9904 + 0.500000i 0.576923 + 0.0222058i
\(508\) 12.6603i 0.561708i
\(509\) −25.3923 14.6603i −1.12549 0.649804i −0.182696 0.983169i \(-0.558483\pi\)
−0.942798 + 0.333365i \(0.891816\pi\)
\(510\) 0 0
\(511\) −10.3923 18.0000i −0.459728 0.796273i
\(512\) −1.00000 −0.0441942
\(513\) −2.86603 4.96410i −0.126538 0.219170i
\(514\) 12.5885 7.26795i 0.555253 0.320575i
\(515\) 0 0
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) −1.50000 0.866025i −0.0659699 0.0380878i
\(518\) 8.89230 15.4019i 0.390705 0.676722i
\(519\) −2.12436 −0.0932489
\(520\) 0 0
\(521\) −6.60770 −0.289488 −0.144744 0.989469i \(-0.546236\pi\)
−0.144744 + 0.989469i \(0.546236\pi\)
\(522\) 0.732051 1.26795i 0.0320410 0.0554966i
\(523\) 36.1244 + 20.8564i 1.57961 + 0.911987i 0.994913 + 0.100733i \(0.0321189\pi\)
0.584694 + 0.811254i \(0.301214\pi\)
\(524\) −7.16025 12.4019i −0.312797 0.541781i
\(525\) 0 0
\(526\) 21.2321 12.2583i 0.925761 0.534489i
\(527\) −9.85641 17.0718i −0.429352 0.743659i
\(528\) −0.267949 −0.0116610
\(529\) −5.50000 9.52628i −0.239130 0.414186i
\(530\) 0 0
\(531\) 9.92820 + 5.73205i 0.430847 + 0.248750i
\(532\) 17.1962i 0.745548i
\(533\) 13.8564 + 4.00000i 0.600188 + 0.173259i
\(534\) 14.1244 0.611221
\(535\) 0 0
\(536\) −0.732051 + 1.26795i −0.0316198 + 0.0547671i
\(537\) 7.85641 4.53590i 0.339029 0.195738i
\(538\) −17.0718 −0.736017
\(539\) −0.464102 + 0.267949i −0.0199903 + 0.0115414i
\(540\) 0 0
\(541\) 14.7846i 0.635640i −0.948151 0.317820i \(-0.897049\pi\)
0.948151 0.317820i \(-0.102951\pi\)
\(542\) 21.1244 12.1962i 0.907369 0.523870i
\(543\) 14.6603 + 8.46410i 0.629132 + 0.363229i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) 10.3923 + 3.00000i 0.444750 + 0.128388i
\(547\) 5.32051i 0.227488i 0.993510 + 0.113744i \(0.0362844\pi\)
−0.993510 + 0.113744i \(0.963716\pi\)
\(548\) −6.73205 + 11.6603i −0.287579 + 0.498101i
\(549\) −0.267949 + 0.464102i −0.0114358 + 0.0198074i
\(550\) 0 0
\(551\) 8.39230i 0.357524i
\(552\) 1.73205 + 3.00000i 0.0737210 + 0.127688i
\(553\) 4.60770 + 7.98076i 0.195939 + 0.339377i
\(554\) 11.5885i 0.492346i
\(555\) 0 0
\(556\) −9.89230 + 17.1340i −0.419527 + 0.726642i
\(557\) −11.3038 + 19.5788i −0.478959 + 0.829582i −0.999709 0.0241275i \(-0.992319\pi\)
0.520749 + 0.853710i \(0.325653\pi\)
\(558\) 4.92820i 0.208627i
\(559\) −15.5885 + 15.0000i −0.659321 + 0.634432i
\(560\) 0 0
\(561\) −0.928203 0.535898i −0.0391888 0.0226256i
\(562\) −6.00000 3.46410i −0.253095 0.146124i
\(563\) −13.2679 + 7.66025i −0.559177 + 0.322841i −0.752815 0.658232i \(-0.771305\pi\)
0.193638 + 0.981073i \(0.437971\pi\)
\(564\) 6.46410i 0.272188i
\(565\) 0 0
\(566\) 5.53590 3.19615i 0.232691 0.134344i
\(567\) 3.00000 0.125988
\(568\) 11.1962 6.46410i 0.469780 0.271228i
\(569\) −8.16025 + 14.1340i −0.342096 + 0.592527i −0.984822 0.173569i \(-0.944470\pi\)
0.642726 + 0.766096i \(0.277803\pi\)
\(570\) 0 0
\(571\) 10.8564 0.454326 0.227163 0.973857i \(-0.427055\pi\)
0.227163 + 0.973857i \(0.427055\pi\)
\(572\) 0.232051 + 0.937822i 0.00970253 + 0.0392123i
\(573\) 17.3205i 0.723575i
\(574\) 10.3923 + 6.00000i 0.433766 + 0.250435i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 9.32051 0.388018 0.194009 0.981000i \(-0.437851\pi\)
0.194009 + 0.981000i \(0.437851\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) 8.53590 4.92820i 0.354740 0.204809i
\(580\) 0 0
\(581\) 14.1962 + 24.5885i 0.588956 + 1.02010i
\(582\) −7.26795 4.19615i −0.301266 0.173936i
\(583\) 0.0358984 0.0621778i 0.00148676 0.00257514i
\(584\) −6.92820 −0.286691
\(585\) 0 0
\(586\) 29.2487 1.20825
\(587\) −4.46410 + 7.73205i −0.184253 + 0.319136i −0.943325 0.331871i \(-0.892320\pi\)
0.759071 + 0.651007i \(0.225653\pi\)
\(588\) 1.73205 + 1.00000i 0.0714286 + 0.0412393i
\(589\) −14.1244 24.4641i −0.581984 1.00803i
\(590\) 0 0
\(591\) −9.86603 + 5.69615i −0.405834 + 0.234308i
\(592\) −2.96410 5.13397i −0.121824 0.211005i
\(593\) −44.7846 −1.83908 −0.919542 0.392992i \(-0.871440\pi\)
−0.919542 + 0.392992i \(0.871440\pi\)
\(594\) 0.133975 + 0.232051i 0.00549704 + 0.00952116i
\(595\) 0 0
\(596\) 16.2679 + 9.39230i 0.666361 + 0.384724i
\(597\) 24.9282i 1.02024i
\(598\) 9.00000 8.66025i 0.368037 0.354144i
\(599\) −28.9282 −1.18197 −0.590987 0.806681i \(-0.701262\pi\)
−0.590987 + 0.806681i \(0.701262\pi\)
\(600\) 0 0
\(601\) −15.3564 + 26.5981i −0.626401 + 1.08496i 0.361867 + 0.932230i \(0.382139\pi\)
−0.988268 + 0.152729i \(0.951194\pi\)
\(602\) −15.5885 + 9.00000i −0.635338 + 0.366813i
\(603\) 1.46410 0.0596228
\(604\) 19.7321 11.3923i 0.802886 0.463546i
\(605\) 0 0
\(606\) 12.3923i 0.503403i
\(607\) 18.5718 10.7224i 0.753806 0.435210i −0.0732615 0.997313i \(-0.523341\pi\)
0.827067 + 0.562103i \(0.190007\pi\)
\(608\) −4.96410 2.86603i −0.201321 0.116233i
\(609\) −3.80385 2.19615i −0.154140 0.0889926i
\(610\) 0 0
\(611\) 22.6244 5.59808i 0.915283 0.226474i
\(612\) 4.00000i 0.161690i
\(613\) −22.5000 + 38.9711i −0.908766 + 1.57403i −0.0929864 + 0.995667i \(0.529641\pi\)
−0.815780 + 0.578362i \(0.803692\pi\)
\(614\) 14.1244 24.4641i 0.570013 0.987291i
\(615\) 0 0
\(616\) 0.803848i 0.0323879i
\(617\) 17.7321 + 30.7128i 0.713865 + 1.23645i 0.963395 + 0.268084i \(0.0863905\pi\)
−0.249530 + 0.968367i \(0.580276\pi\)
\(618\) −5.79423 10.0359i −0.233078 0.403703i
\(619\) 2.51666i 0.101153i 0.998720 + 0.0505766i \(0.0161059\pi\)
−0.998720 + 0.0505766i \(0.983894\pi\)
\(620\) 0 0
\(621\) 1.73205 3.00000i 0.0695048 0.120386i
\(622\) 9.46410 16.3923i 0.379476 0.657272i
\(623\) 42.3731i 1.69764i
\(624\) 2.59808 2.50000i 0.104006 0.100080i
\(625\) 0 0
\(626\) −28.8564 16.6603i −1.15333 0.665878i
\(627\) −1.33013 0.767949i −0.0531202 0.0306689i
\(628\) −18.3564 + 10.5981i −0.732500 + 0.422909i
\(629\) 23.7128i 0.945492i
\(630\) 0 0
\(631\) −6.92820 + 4.00000i −0.275807 + 0.159237i −0.631524 0.775356i \(-0.717570\pi\)
0.355716 + 0.934594i \(0.384237\pi\)
\(632\) 3.07180 0.122190
\(633\) 6.99038 4.03590i 0.277843 0.160413i
\(634\) −15.2321 + 26.3827i −0.604942 + 1.04779i
\(635\) 0 0
\(636\) −0.267949 −0.0106249
\(637\) 2.00000 6.92820i 0.0792429 0.274505i
\(638\) 0.392305i 0.0155315i
\(639\) −11.1962 6.46410i −0.442913 0.255716i
\(640\) 0 0
\(641\) −7.23205 12.5263i −0.285649 0.494758i 0.687117 0.726546i \(-0.258876\pi\)
−0.972766 + 0.231788i \(0.925542\pi\)
\(642\) −12.9282 −0.510235
\(643\) 6.39230 + 11.0718i 0.252088 + 0.436629i 0.964100 0.265538i \(-0.0855495\pi\)
−0.712013 + 0.702167i \(0.752216\pi\)
\(644\) 9.00000 5.19615i 0.354650 0.204757i
\(645\) 0 0
\(646\) −11.4641 19.8564i −0.451049 0.781240i
\(647\) −30.9449 17.8660i −1.21657 0.702386i −0.252386 0.967627i \(-0.581215\pi\)
−0.964182 + 0.265241i \(0.914549\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 3.07180 0.120579
\(650\) 0 0
\(651\) 14.7846 0.579455
\(652\) −1.46410 + 2.53590i −0.0573386 + 0.0993134i
\(653\) 1.37564 + 0.794229i 0.0538331 + 0.0310806i 0.526675 0.850067i \(-0.323438\pi\)
−0.472842 + 0.881147i \(0.656772\pi\)
\(654\) 5.19615 + 9.00000i 0.203186 + 0.351928i
\(655\) 0 0
\(656\) 3.46410 2.00000i 0.135250 0.0780869i
\(657\) 3.46410 + 6.00000i 0.135147 + 0.234082i
\(658\) 19.3923 0.755991
\(659\) −19.8564 34.3923i −0.773496 1.33973i −0.935636 0.352966i \(-0.885173\pi\)
0.162140 0.986768i \(-0.448160\pi\)
\(660\) 0 0
\(661\) −18.7128 10.8038i −0.727844 0.420221i 0.0897889 0.995961i \(-0.471381\pi\)
−0.817633 + 0.575740i \(0.804714\pi\)
\(662\) 14.3923i 0.559373i
\(663\) 14.0000 3.46410i 0.543715 0.134535i
\(664\) 9.46410 0.367278
\(665\) 0 0
\(666\) −2.96410 + 5.13397i −0.114857 + 0.198937i
\(667\) −4.39230 + 2.53590i −0.170071 + 0.0981904i
\(668\) 0.464102 0.0179566
\(669\) 16.3301 9.42820i 0.631359 0.364515i
\(670\) 0 0
\(671\) 0.143594i 0.00554337i
\(672\) 2.59808 1.50000i 0.100223 0.0578638i
\(673\) 14.5359 + 8.39230i 0.560318 + 0.323500i 0.753273 0.657708i \(-0.228474\pi\)
−0.192955 + 0.981208i \(0.561807\pi\)
\(674\) 22.8564 + 13.1962i 0.880396 + 0.508297i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 10.9282i 0.420005i −0.977701 0.210002i \(-0.932653\pi\)
0.977701 0.210002i \(-0.0673472\pi\)
\(678\) −6.00000 + 10.3923i −0.230429 + 0.399114i
\(679\) −12.5885 + 21.8038i −0.483101 + 0.836755i
\(680\) 0 0
\(681\) 6.53590i 0.250456i
\(682\) 0.660254 + 1.14359i 0.0252824 + 0.0437905i
\(683\) 20.6603 + 35.7846i 0.790543 + 1.36926i 0.925631 + 0.378427i \(0.123535\pi\)
−0.135089 + 0.990834i \(0.543132\pi\)
\(684\) 5.73205i 0.219170i
\(685\) 0 0
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) 2.26795 3.92820i 0.0865277 0.149870i
\(688\) 6.00000i 0.228748i
\(689\) 0.232051 + 0.937822i 0.00884043 + 0.0357282i
\(690\) 0 0
\(691\) 13.0359 + 7.52628i 0.495909 + 0.286313i 0.727023 0.686614i \(-0.240904\pi\)
−0.231114 + 0.972927i \(0.574237\pi\)
\(692\) 1.83975 + 1.06218i 0.0699366 + 0.0403779i
\(693\) 0.696152 0.401924i 0.0264446 0.0152678i
\(694\) 4.39230i 0.166730i
\(695\) 0 0
\(696\) −1.26795 + 0.732051i −0.0480615 + 0.0277483i
\(697\) 16.0000 0.606043
\(698\) 9.12436 5.26795i 0.345362 0.199395i
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 0 0
\(701\) −4.39230 −0.165895 −0.0829475 0.996554i \(-0.526433\pi\)
−0.0829475 + 0.996554i \(0.526433\pi\)
\(702\) −3.46410 1.00000i −0.130744 0.0377426i
\(703\) 33.9808i 1.28161i
\(704\) 0.232051 + 0.133975i 0.00874574 + 0.00504936i
\(705\) 0 0
\(706\) 3.80385 + 6.58846i 0.143160 + 0.247960i
\(707\) 37.1769 1.39818
\(708\) −5.73205 9.92820i −0.215424 0.373125i
\(709\) 23.6603 13.6603i 0.888579 0.513022i 0.0151019 0.999886i \(-0.495193\pi\)
0.873478 + 0.486864i \(0.161859\pi\)
\(710\) 0 0
\(711\) −1.53590 2.66025i −0.0576007 0.0997673i
\(712\) −12.2321 7.06218i −0.458415 0.264666i
\(713\) 8.53590 14.7846i 0.319672 0.553688i
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) −9.07180 −0.339029
\(717\) −1.73205 + 3.00000i −0.0646846 + 0.112037i
\(718\) 0.803848 + 0.464102i 0.0299993 + 0.0173201i
\(719\) 8.00000 + 13.8564i 0.298350 + 0.516757i 0.975759 0.218850i \(-0.0702305\pi\)
−0.677409 + 0.735607i \(0.736897\pi\)
\(720\) 0 0
\(721\) −30.1077 + 17.3827i −1.12127 + 0.647365i
\(722\) −6.92820 12.0000i −0.257841 0.446594i
\(723\) −25.1962 −0.937055
\(724\) −8.46410 14.6603i −0.314566 0.544844i
\(725\) 0 0
\(726\) −9.46410 5.46410i −0.351246 0.202792i
\(727\) 4.66025i 0.172839i 0.996259 + 0.0864196i \(0.0275426\pi\)
−0.996259 + 0.0864196i \(0.972457\pi\)
\(728\) −7.50000 7.79423i −0.277968 0.288873i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 0.464102 0.267949i 0.0171537 0.00990369i
\(733\) 20.8564 0.770349 0.385174 0.922844i \(-0.374141\pi\)
0.385174 + 0.922844i \(0.374141\pi\)
\(734\) 18.4641 10.6603i 0.681522 0.393477i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) 0.339746 0.196152i 0.0125147 0.00722537i
\(738\) −3.46410 2.00000i −0.127515 0.0736210i
\(739\) −31.0359 17.9186i −1.14167 0.659146i −0.194829 0.980837i \(-0.562415\pi\)
−0.946845 + 0.321691i \(0.895749\pi\)
\(740\) 0 0
\(741\) 20.0622 4.96410i 0.737003 0.182361i
\(742\) 0.803848i 0.0295102i
\(743\) 5.46410 9.46410i 0.200458 0.347204i −0.748218 0.663453i \(-0.769090\pi\)
0.948676 + 0.316249i \(0.102424\pi\)
\(744\) 2.46410 4.26795i 0.0903383 0.156471i
\(745\) 0 0
\(746\) 9.07180i 0.332142i
\(747\) −4.73205 8.19615i −0.173137 0.299882i
\(748\) 0.535898 + 0.928203i 0.0195944 + 0.0339385i
\(749\) 38.7846i 1.41716i
\(750\) 0 0
\(751\) 10.5885 18.3397i 0.386378 0.669227i −0.605581 0.795784i \(-0.707059\pi\)
0.991959 + 0.126557i \(0.0403926\pi\)
\(752\) 3.23205 5.59808i 0.117861 0.204141i
\(753\) 19.5359i 0.711928i
\(754\) 3.66025 + 3.80385i 0.133299 + 0.138528i
\(755\) 0 0
\(756\) −2.59808 1.50000i −0.0944911 0.0545545i
\(757\) 18.8205 + 10.8660i 0.684043 + 0.394932i 0.801377 0.598160i \(-0.204101\pi\)
−0.117334 + 0.993093i \(0.537435\pi\)
\(758\) 8.42820 4.86603i 0.306126 0.176742i
\(759\) 0.928203i 0.0336916i
\(760\) 0 0
\(761\) 6.91154 3.99038i 0.250543 0.144651i −0.369470 0.929243i \(-0.620461\pi\)
0.620013 + 0.784592i \(0.287127\pi\)
\(762\) −12.6603 −0.458633
\(763\) 27.0000 15.5885i 0.977466 0.564340i
\(764\) 8.66025 15.0000i 0.313317 0.542681i
\(765\) 0 0
\(766\) 4.78461 0.172875
\(767\) −29.7846 + 28.6603i −1.07546 + 1.03486i
\(768\) 1.00000i 0.0360844i
\(769\) −13.6077 7.85641i −0.490706 0.283309i 0.234161 0.972198i \(-0.424766\pi\)
−0.724867 + 0.688889i \(0.758099\pi\)
\(770\) 0 0
\(771\) 7.26795 + 12.5885i 0.261749 + 0.453362i
\(772\) −9.85641 −0.354740
\(773\) −16.3038 28.2391i −0.586409 1.01569i −0.994698 0.102837i \(-0.967208\pi\)
0.408290 0.912852i \(-0.366125\pi\)
\(774\) 5.19615 3.00000i 0.186772 0.107833i
\(775\) 0 0
\(776\) 4.19615 + 7.26795i 0.150633 + 0.260904i
\(777\) 15.4019 + 8.89230i 0.552541 + 0.319010i
\(778\) −8.92820 + 15.4641i −0.320092 + 0.554415i
\(779\) 22.9282 0.821488
\(780\) 0 0
\(781\) −3.46410 −0.123955
\(782\) 6.92820 12.0000i 0.247752 0.429119i
\(783\) 1.26795 + 0.732051i 0.0453128 +